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통계

Misha 在笔记本上写下了几个他认为“美丽”的整数,然后去玩加号和减号了。他认为一个由加号和减号组成的字符串是“平衡的”,如果它包含相同数量的加号和减号,且末尾连续的减号个数是一个美丽的整数。对于长度为 $2, 4, \dots, 2n$ 的字符串,分别有多少个平衡字符串?由于答案可能非常大,请将它们对 $998\,244\,353$ 取模后输出。

输入格式

第一行包含两个整数 $n$ 和 $m$,分别表示最大长度参数和 Misha 笔记本中整数的个数($1 \le n, m \le 200\,000$)。

第二行包含 $m$ 个互不相同的非负整数,范围在 $[0, n]$ 内,表示 Misha 笔记本中的数字。

输出格式

输出 $n$ 行,表示对 $998\,244\,353$ 取模后的答案。

样例

输入样例 1

5 3
1 2 3

输出样例 1

1
3
10
34
120

Editorials

IDTypeStatusTitlePosted ByLast UpdatedActions
#1537EditorialOpenNew Editorial for Problem #17166Xuan01092026-04-15 17:47:21View
#1217EditorialOpen题解jiangly2026-03-06 01:29:36View
#1081EditorialOpenNew Editorial for Problem #17166GotoHiotori2026-02-22 10:10:29View

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